How can I express a thought of a distance between two cities measured as a length of a line segment connecting them on a map, as opposite to distance of the two cities measured as length of a road connecting them?
a) in a straight line
b) as the crow flies
c) length of beeline
context: Distance between Paris and Rome is 1104 km measured in a straight line.
"As the crow flies" works here. Wiktionary defines it as:
In a straight line distance between two locations, as opposed to the road distance or over land distance.
From that definition, "in a straight line" would also work. However, strictly speaking the distance between two points over Earth's surface is not a line but a geodesic (see Wikipedia), so I would take "in a straight line" to be (if we are being extremely pedantic) misleading. The length of the line segment between two points on a map depends entirely on the map projection in use, and this itself differs from the straight-line distance between two points, since such a line could go beneath the Earth's surface.
These distinctions are particularly important over long distances where such discrepancies become larger. You usually care about the geodesic distance, since that determines travel time. "As the crow flies" presumably refers to geodesic distances, since it is based on the idea that a crow would take the shortest route over Earth's surface.
The word "beeline" is used primarily in the idiom "make a beeline for"; per Merriam-Webster, "beeline" refers to a straight, direct course. But it does not appear to refer unambiguously to the geodesic distance.
